/* HandmadeMath.h v0.1 This is a single header file with a bunch of useful functions for basic game math operations. ========================================================================== You MUST #define HANDMADE_MATH_IMPLEMENTATION in EXACTLY one C or C++ file that includes this header, BEFORE the include, like this: #define HANDMADE_MATH_IMPLEMENTATION #include "HandmadeMath.h" All other files should just #include "HandmadeMath.h" without the #define. ========================================================================== For overloaded, and operator overloaded versions of the base C functions. You MUST #define HANDMADE_MATH_CPP_MODE in EXACTLY one C or C++ file that includes this header, BEFORE the include, like this: #define HANDMADE_MATH_IMPLEMENTATION #define HANDMADE_MATH_CPP_MODE #include "HandmadeMath.h" All other files should just #include "HandmadeMath.h" without the #define. ========================================================================== LICENSE This software is in the public domain. Where that dedication is not recognized, you are granted a perpetual, irrevocable license to copy, distribute, and modify this file as you see fit. CREDITS Written by Zakary Strange (zak@strangedev.net && @strangezak) Functionality: Matt Mascarenhas (@miblo_) Fixes: Jeroen van Rijn (@J_vanRijn) Kiljacken (@Kiljacken) Insofaras (@insofaras) */ #ifndef HANDMADE_MATH_H #define HANDMADE_MATH_H // TODO(zak): Make some sort of documentation for this and a way to remove it #include #ifdef __cplusplus extern "C" { #endif #ifdef HANDMADEMATH_STATIC #define HMMDEF static #else #define HMMDEF extern #endif #if _MSC_VER && !__INTEL_COMPILER #define HINLINE __inline #else #define HINLINE inline #endif #define Pi32 3.14159265359f #define HMM_PI 3.14159265358979323846 typedef union vec2 { struct { float X, Y; }; struct { float U, V; }; struct { float Left, Right; }; float Elements[2]; } vec2; typedef union vec3 { struct { float X, Y, Z; }; struct { float U, V, W; }; struct { float R, G, B; }; struct { vec2 XY; float Ignored0_; }; struct { float Ignored1_; vec2 YZ; }; struct { vec2 UV; float Ignored2_; }; struct { float Ignored3_; vec2 VW; }; float Elements[3]; } vec3; typedef union vec4 { struct { union { vec3 XYZ; struct { float X, Y, Z; }; }; float W; }; struct { union { vec3 RGB; struct { float R, G, B; }; }; float A; }; struct { vec2 XY; float Ignored0_; float Ignored1_; }; struct { float Ignored2_; vec2 YZ; float Ignored3_; }; struct { float Ignored4_; float Ignored5_; vec2 ZW; }; float Elements[4]; } vec4; typedef union mat4 { float Elements[4][4]; } mat4; HMMDEF HINLINE float Power(float Base, int Exponent); HMMDEF HINLINE float Clamp(float Min, float Value, float Max); HMMDEF HINLINE vec3 Normalize(vec3 A); HMMDEF HINLINE vec3 Cross(vec3 VecOne, vec3 VecTwo); HMMDEF HINLINE float Dot(vec3 VecOne, vec3 VecTwo); HMMDEF HINLINE vec2 Vec2i(int X, int Y); HMMDEF HINLINE vec2 Vec2(float X, float Y); HMMDEF HINLINE vec3 Vec3(float X, float Y, float Z); HMMDEF HINLINE vec3 Vec3i(int X, int Y, int Z); HMMDEF HINLINE vec4 Vec4(float X, float Y, float Z, float W); HMMDEF HINLINE vec4 Vec4i(int X, int Y, int Z, int W); HMMDEF HINLINE vec2 AddVec2(vec2 Left, vec2 Right); HMMDEF HINLINE vec3 AddVec3(vec3 Left, vec3 Right); HMMDEF HINLINE vec4 AddVec4(vec4 Left, vec4 Right); HMMDEF HINLINE vec2 SubtractVec2(vec2 Left, vec2 Right); HMMDEF HINLINE vec3 SubtractVec3(vec3 Left, vec3 Right); HMMDEF HINLINE vec4 SubtractVec4(vec4 Left, vec4 Right); HMMDEF HINLINE vec2 MultiplyVec2(vec2 Left, vec2 Right); HMMDEF HINLINE vec3 MultiplyVec3(vec3 Left, vec3 Right); HMMDEF HINLINE vec4 MultiplyVec4(vec4 Left, vec4 Right); HMMDEF HINLINE vec2 DivideVec2(vec2 Left, vec2 Right); HMMDEF HINLINE vec3 DivideVec3(vec3 Left, vec3 Right); HMMDEF HINLINE vec4 DivideVec4(vec4 Left, vec4 Right); HMMDEF mat4 Mat4(void); HMMDEF mat4 Mat4d(float Diagonal); HMMDEF mat4 MultiplyMat4(mat4 Left, mat4 Right); HMMDEF mat4 Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far); HMMDEF mat4 Perspective(float FOV, float AspectRatio, float Near, float Far); HMMDEF mat4 Translate(vec3 Translation); HMMDEF mat4 Rotate(float Angle, vec3 Axis); HMMDEF mat4 Scale(vec3 Scale); HMMDEF mat4 LookAt(vec3 Eye, vec3 Center, vec3 Up); #ifdef __cplusplus } #endif #ifdef HANDMADE_MATH_CPP_MODE HMMDEF HINLINE vec2 Add(int X, int Y); HMMDEF HINLINE vec3 Add(int X, int Y, int Z); HMMDEF HINLINE vec4 Add(int X, int Y, int Z, int W); HMMDEF HINLINE vec2 Subtract(int X, int Y); HMMDEF HINLINE vec3 Subtract(int X, int Y, int Z); HMMDEF HINLINE vec4 Subtract(int X, int Y, int Z, int W); HMMDEF HINLINE vec2 Multiply(int X, int Y); HMMDEF HINLINE vec3 Multiply(int X, int Y, int Z); HMMDEF HINLINE vec4 Multiply(int X, int Y, int Z, int W); HMMDEF HINLINE mat4 Multiply(mat4 Left, mat4 Right); HMMDEF HINLINE vec2 Divide(int X, int Y); HMMDEF HINLINE vec3 Divide(int X, int Y, int Z); HMMDEF HINLINE vec4 Divide(int X, int Y, int Z, int W); HMMDEF vec2 operator+(vec2 Left, vec2 Right); HMMDEF vec3 operator+(vec3 Left, vec3 Right); HMMDEF vec4 operator+(vec4 Left, vec4 Right); HMMDEF vec2 operator-(vec2 Left, vec2 Right); HMMDEF vec3 operator-(vec3 Left, vec3 Right); HMMDEF vec4 operator-(vec4 Left, vec4 Right); HMMDEF vec2 operator*(vec2 Left, vec2 Right); HMMDEF vec3 operator*(vec3 Left, vec3 Right); HMMDEF vec4 operator*(vec4 Left, vec4 Right); HMMDEF mat4 operator*(mat4 Left, mat4 Right); HMMDEF vec3 operator*(vec3 Left, float Right); HMMDEF vec2 operator/(vec2 Left, vec2 Right); HMMDEF vec3 operator/(vec3 Left, vec3 Right); HMMDEF vec4 operator/(vec4 Left, vec4 Right); #endif /* HANDMADE_MATH_CPP */ #endif /* HANDMADE_MATH_H */ #ifdef HANDMADE_MATH_IMPLEMENTATION HMMDEF HINLINE float ToRadians(float Degrees) { float Result = Degrees * (Pi32 / 180.0f); return(Result); } HMMDEF HINLINE float Inner(vec3 A, vec3 B) { float Result = A.X*B.X + A.Y*B.Y + A.Z*B.Z; return(Result); } HMMDEF HINLINE float SquareRoot(float Float) { float Result = sqrtf(Float); return(Result); } HMMDEF HINLINE float LengthSq(vec3 A) { float Result = Inner(A, A); return(Result); } HMMDEF HINLINE float Length(vec3 A) { float Result = SquareRoot(LengthSq(A)); return(Result); } HMMDEF HINLINE float Power(float Base, int Exponent) { float Result = 1; if (Exponent > 0) { for (int i = 0; i < Exponent; ++i) { Result *= Base; } } else { for (int i = 0; i > Exponent; --i) { Result /= Base; } } return (Result); } HMMDEF HINLINE float Lerp(float A, float Time, float B) { float Result = (1.0f - Time) * A + Time * B; return(Result); } HMMDEF HINLINE float Clamp(float Min, float Value, float Max) { float Result = Value; if(Result < Min) { Result = Min; } else if(Result > Max) { Result = Max; } return(Result); } HMMDEF HINLINE vec3 Normalize(vec3 A) { vec3 Result = A * (1.0f / Length(A)); return(Result); } HMMDEF HINLINE vec3 Cross(vec3 VecOne, vec3 VecTwo) { vec3 Result; Result.X = (VecOne.Y * VecTwo.Z) - (VecOne.Z * VecTwo.Y); Result.Y = (VecOne.Z * VecTwo.X) - (VecOne.X * VecTwo.Z); Result.Z = (VecOne.X * VecTwo.Y) - (VecOne.Y * VecTwo.X); return(Result); } HMMDEF HINLINE float Dot(vec3 VecOne, vec3 VecTwo) { float Result = 0; Result = (VecOne.X * VecTwo.X) + (VecOne.Y * VecTwo.Y) + (VecOne.Z * VecTwo.Z); return(Result); } HMMDEF HINLINE vec2 Vec2(float X, float Y) { vec2 Result; Result.X = X; Result.Y = Y; return(Result); } HMMDEF HINLINE vec2 Vec2i(int X, int Y) { vec2 Result; Result.X = (float)X; Result.Y = (float)Y; return(Result); } HMMDEF HINLINE vec3 Vec3(float X, float Y, float Z) { vec3 Result; Result.X = X; Result.Y = Y; Result.Z = Z; return(Result); } HMMDEF HINLINE vec3 Vec3i(int X, int Y, int Z) { vec3 Result; Result.X = (float)X; Result.Y = (float)Y; Result.Z = (float)Z; return(Result); } HMMDEF HINLINE vec4 Vec4(float X, float Y, float Z, float W) { vec4 Result; Result.X = X; Result.Y = Y; Result.Z = Z; Result.W = W; return(Result); } HMMDEF HINLINE vec4 Vec4i(int X, int Y, int Z, int W) { vec4 Result; Result.X = (float)X; Result.Y = (float)Y; Result.Z = (float)Z; Result.W = (float)W; return(Result); } HMMDEF HINLINE vec2 AddVec2(vec2 Left, vec2 Right) { vec2 Result; Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; return(Result); } HMMDEF HINLINE vec3 AddVec3(vec3 Left, vec3 Right) { vec3 Result; Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; Result.Z = Left.Z + Right.Z; return(Result); } HMMDEF HINLINE vec4 AddVec4(vec4 Left, vec4 Right) { vec4 Result; Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; Result.Z = Left.Z + Right.Z; Result.W = Left.W + Right.W; return(Result); } HMMDEF HINLINE vec2 SubtractVec2(vec2 Left, vec2 Right) { vec2 Result; Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; return(Result); } HMMDEF HINLINE vec3 SubtractVec3(vec3 Left, vec3 Right) { vec3 Result; Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; Result.Z = Left.Z - Right.Z; return(Result); } HMMDEF HINLINE vec4 SubtractVec4(vec4 Left, vec4 Right) { vec4 Result; Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; Result.Z = Left.Z - Right.Z; Result.W = Left.W - Right.W; return(Result); } HMMDEF HINLINE vec2 MultiplyVec2(vec2 Left, vec2 Right) { vec2 Result; Result.X = Left.X * Right.X; Result.Y = Left.Y * Right.Y; return(Result); } HMMDEF HINLINE vec3 MultiplyVec3(vec3 Left, vec3 Right) { vec3 Result; Result.X = Left.Z * Right.X; Result.Y = Left.Y * Right.Y; Result.Z = Left.Z * Right.Z; return(Result); } HMMDEF HINLINE vec4 MultiplyVec4(vec4 Left, vec4 Right) { vec4 Result; Result.X = Left.X * Right.X; Result.Y = Left.Y * Right.Y; Result.Z = Left.Z * Right.Z; Result.W = Left.W * Right.W; return(Result); } HMMDEF HINLINE vec2 DivideVec2(vec2 Left, vec2 Right) { vec2 Result; Result.X = Left.X / Right.X; Result.Y = Left.Y / Right.Y; return(Result); } HMMDEF HINLINE vec3 DivideVec3(vec3 Left, vec3 Right) { vec3 Result; Result.X = Left.X / Right.X; Result.Y = Left.Y / Right.Y; Result.Z = Left.Z / Right.Z; return(Result); } HMMDEF HINLINE vec4 DivideVec4(vec4 Left, vec4 Right) { vec4 Result; Result.X = Left.X / Right.X; Result.Y = Left.Y / Right.Y; Result.Z = Left.Z / Right.Z; Result.W = Left.W / Right.W; return(Result); } HMMDEF mat4 Mat4() { mat4 Result; for(int Rows = 0; Rows < 4; ++Rows) { for(int Columns = 0; Columns < 4; ++Columns) { Result.Elements[Rows][Columns] = 0.0f; } } return(Result); } HMMDEF mat4 Mat4d(float Diagonal) { mat4 Result; for(int Rows = 0; Rows < 4; ++Rows) { for(int Columns = 0; Columns < 4; ++Columns) { Result.Elements[Rows][Columns] = 0.0f; } } Result.Elements[0][0] = Diagonal; Result.Elements[1][1] = Diagonal; Result.Elements[2][2] = Diagonal; Result.Elements[3][3] = Diagonal; return(Result); } HMMDEF mat4 MultiplyMat4(mat4 Left, mat4 Right) { mat4 Result = Mat4(); for(int Rows = 0; Rows < 4; ++Rows) { for(int Columns = 0; Columns < 4; ++Columns) { float Sum = 0; for(int CurrentMatrice = 0; CurrentMatrice < 4; ++CurrentMatrice) { Sum += Right.Elements[Rows][CurrentMatrice] * Left.Elements[CurrentMatrice][Columns]; } Result.Elements[Columns][Rows] = Sum; } } return(Result); } HMMDEF mat4 Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far) { mat4 Result = Mat4d(1.0f); Result.Elements[0][0] = 2.0f / (Right - Left); Result.Elements[1][1] = 2.0f / (Top - Bottom); Result.Elements[2][2] = 2.0f / (Near - Far); Result.Elements[0][3] = (Left + Right) / (Left - Right); Result.Elements[1][3] = (Bottom + Top) / (Bottom - Top); Result.Elements[2][3] = (Far + Near) / (Far - Near); return(Result); } HMMDEF mat4 Perspective(float FOV, float AspectRatio, float Near, float Far) { mat4 Result = Mat4d(1.0f); Result.Elements[0][0] = 1.0f / (AspectRatio * tan(FOV / 2.0f)); Result.Elements[1][1] = 1.0f / tan(FOV / 2.0f); Result.Elements[2][3] = -1.0f; Result.Elements[2][2] = -(Far + Near) / (Far - Near); Result.Elements[3][2] = -(2.0f * Far * Near) / (Far - Near); Result.Elements[3][3] = 0.0f; return(Result); } HMMDEF mat4 Translate(vec3 Translation) { mat4 Result = Mat4d(1.0f); Result.Elements[0][3] = Translation.X; Result.Elements[1][3] = Translation.Y; Result.Elements[2][3] = Translation.Z; return(Result); } HMMDEF mat4 Rotate(float Angle, vec3 Axis) { mat4 Result = Mat4d(1.0f); Result.Elements[0][0] = Axis.Z * (1.0f - cos(ToRadians(Angle))) + cos(ToRadians(Angle)); Result.Elements[1][0] = Axis.Y * Axis.X * (1.0f - cos(ToRadians(Angle))) + Axis.Z * (sin(ToRadians(Angle))); Result.Elements[2][0] = Axis.X * Axis.Z * (1.0f - cos(ToRadians(Angle))) - Axis.Y * (sin(ToRadians(Angle))); Result.Elements[0][1] = Axis.X * Axis.Y * (1.0f - cos(ToRadians(Angle))) - Axis.Z * (sin(ToRadians(Angle))); Result.Elements[1][1] = Axis.Y * (1.0f - cos(ToRadians(Angle))) + (cos(ToRadians(Angle))); Result.Elements[2][1] = Axis.Y * Axis.Z * (1.0f - cos(ToRadians(Angle))) + Axis.X * (sin(ToRadians(Angle))); Result.Elements[0][2] = Axis.X * Axis.Z * (1.0f - cos(ToRadians(Angle))) + Axis.Y * (sin(ToRadians(Angle))); Result.Elements[1][2] = Axis.Y * Axis.Z * (1.0f - cos(ToRadians(Angle))) - Axis.X * (sin(ToRadians(Angle))); Result.Elements[2][2] = Axis.Z * (1.0f - cos(ToRadians(Angle))) * (cos(ToRadians(Angle))); return(Result); } HMMDEF mat4 LookAt(vec3 Eye, vec3 Center, vec3 Up) { mat4 Result = {}; vec3 F = Normalize(Center - Eye); vec3 S = Normalize(Cross(F, Up)); vec3 U = Cross(S, F); Result.Elements[0][0] = S.X; Result.Elements[0][1] = U.X; Result.Elements[0][2] = -F.X; Result.Elements[1][0] = S.Y; Result.Elements[1][1] = U.Y; Result.Elements[1][2] = -F.Y; Result.Elements[2][0] = S.Z; Result.Elements[2][1] = U.Z; Result.Elements[2][2] = -F.Z; Result.Elements[3][0] = -Dot(S, Eye); Result.Elements[3][1] = -Dot(U, Eye); Result.Elements[3][2] = Dot(F, Eye); Result.Elements[3][3] = 1.0f; return(Result); } HMMDEF mat4 Scale(vec3 Scale) { mat4 Result = Mat4d(1.0f); Result.Elements[0][0] = Scale.X; Result.Elements[1][1] = Scale.Y; Result.Elements[2][2] = Scale.Z; return(Result); } #ifdef HANDMADE_MATH_CPP_MODE HMMDEF HINLINE vec2 Add(vec2 Left, vec2 Right) { vec2 Result = AddVec2(Left, Right); return(Result); } HMMDEF HINLINE vec3 Add(vec3 Left, vec3 Right) { vec3 Result = AddVec3(Left, Right); return(Result); } HMMDEF HINLINE vec4 Add(vec4 Left, vec4 Right) { vec4 Result = AddVec4(Left, Right); return(Result); } HMMDEF HINLINE vec2 Subtract(vec2 Left, vec2 Right) { vec2 Result = SubtractVec2(Left, Right); return(Result); } HMMDEF HINLINE vec3 Subtract(vec3 Left, vec3 Right) { vec3 Result = SubtractVec3(Left, Right); return(Result); } HMMDEF HINLINE vec4 Subtract(vec4 Left, vec4 Right) { vec4 Result = SubtractVec4(Left, Right); return(Result); } HMMDEF HINLINE vec2 Multiply(vec2 Left, vec2 Right) { vec2 Result = MultiplyVec2(Left, Right); return(Result); } HMMDEF HINLINE vec3 Multiply(vec3 Left, vec3 Right) { vec3 Result = MultiplyVec3(Left, Right); return(Result); } HMMDEF HINLINE vec4 Multiply(vec4 Left, vec4 Right) { vec4 Result = MultiplyVec4(Left, Right); return(Result); } HMMDEF HINLINE mat4 Multiply(mat4 Left, mat4 Right) { mat4 Result = MultiplyMat4(Left, Right); return(Result); } HMMDEF HINLINE vec2 Divide(vec2 Left, vec2 Right) { vec2 Result = DivideVec2(Left, Right); return(Result); } HMMDEF HINLINE vec3 Divide(vec3 Left, vec3 Right) { vec3 Result = DivideVec3(Left, Right); return(Result); } HMMDEF HINLINE vec4 Divide(vec4 Left, vec4 Right) { vec4 Result = DivideVec4(Left, Right); return(Result); } HMMDEF HINLINE vec2 operator+(vec2 Left, vec2 Right) { vec2 Result = Add(Left, Right); return(Result); } HMMDEF HINLINE vec3 operator+(vec3 Left, vec3 Right) { vec3 Result = Add(Left, Right); return(Result); } HMMDEF HINLINE vec4 operator+(vec4 Left, vec4 Right) { vec4 Result = Add(Left, Right); return(Result); } HMMDEF HINLINE vec2 operator-(vec2 Left, vec2 Right) { vec2 Result = Subtract(Left, Right); return(Result); } HMMDEF HINLINE vec3 operator-(vec3 Left, vec3 Right) { vec3 Result = Subtract(Left, Right); return(Result); } HMMDEF HINLINE vec4 operator-(vec4 Left, vec4 Right) { vec4 Result = Subtract(Left, Right); return(Result); } HMMDEF HINLINE vec2 operator*(vec2 Left, vec2 Right) { vec2 Result = Multiply(Left, Right); return(Result); } HMMDEF HINLINE vec3 operator*(vec3 Left, vec3 Right) { vec3 Result = Multiply(Left, Right); return(Result); } HMMDEF HINLINE vec3 operator*(vec3 Left, float Right) { vec3 Result; Result.X = Right * Left.X; Result.Y = Right * Left.Y; Result.Z = Right * Left.Z; return(Result); } HMMDEF HINLINE vec4 operator*(vec4 Left, vec4 Right) { vec4 Result = Multiply(Left, Right); return(Result); } HMMDEF HINLINE mat4 operator*(mat4 Left, mat4 Right) { mat4 Result = Multiply(Left, Right); return(Result); } HMMDEF HINLINE vec2 operator/(vec2 Left, vec2 Right) { vec2 Result = Divide(Left, Right); return(Result); } HMMDEF HINLINE vec3 operator/(vec3 Left, vec3 Right) { vec3 Result = Divide(Left, Right); return(Result); } HMMDEF HINLINE vec4 operator/(vec4 Left, vec4 Right) { vec4 Result = Divide(Left, Right); return(Result); } #endif /* HANDMADE_MATH_CPP_MODE */ #endif /* HANDMADE_MATH_IMPLEMENTATION */